A375808 - OEIS

%I #12 Sep 01 2024 10:14:05

%S 1,2,6,24,144,1080,9360,94080,1078560,13789440,194745600,3013718400,

%T 50654419200,918900702720,17896250211840,372338481715200,

%U 8241399758592000,193366506222489600,4793430516921446400,125181207625240166400,3435031723216084992000

%N Expansion of e.g.f. 1/(1 + (log(1 - x^3))/x^2)^2.

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A375799.

%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-3*k+1)! * |Stirling1(n-2*k,n-3*k)|/(n-2*k)!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^3)/x^2)^2))

%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k+1)!*abs(stirling(n-2*k, n-3*k, 1))/(n-2*k)!);

%Y Cf. A375799, A375809.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Aug 29 2024